Simulated Annealing (SA) Algorithm

In this article, we discuss the Simulated Annealing (SA) algorithm. This probabilistic optimization algorithm is designed for solving complex optimization problems. The core concept of SA mimics the physical annealing process in metallurgy, where a material is heated and slowly cooled to reduce defects. In algorithmic terms, this translates to exploring the solution space by gradually lowering a "temperature" parameter, which controls the probability of accepting worse solutions to escape local optima. Temperature scheduling is critical, as it balances exploration and exploitation during the search. Key implementation steps include: generating neighboring solutions, evaluating energy (cost function), and using the Metropolis criterion to accept suboptimal solutions with a probability dependent on temperature. SA also offers advantages like avoidance of local minima and capability to handle nonlinear problems. Consequently, it is widely applied in domains such as image processing, machine learning, and artificial intelligence.